Econ 310, Spring 2014- Week 11:

Problem 1 - A fortune cookie writer calculated the mean and standard deviation from a sample of 51. They are x¯ = 120 and s = 15.

1. Estimate the population mean with 95 percent confidence interval.

2. 90 percent.

3. 80 percent.

4. What is the effect of decreasing the confidence level?

Problem 2 - A citrus fruit dryer randomly sampled 10 observations and found x = 103 and s = 17.

1. Is there sufficient evidence at the 10 percent significance level to conclude that the population mean is less than 110?

2. Repeat Part 1 assuming that you know that the population standard deviation is σ = 17.

3. Are the conclusions different?

Problem 3- A vise president in charges of sales for a large corporation claims that salespeople are averaging no more than 15 sales contacts per week. (He would like to increase this figure.) Based on 36 sample, the mean and variance are 17 and 9, respectively. If he or she wishes to test H₀: µ = 15 against H₁: µ = 16, please find the type II error β in this test.

Problem 4- A company produces machined engine parts that are supposed to have diameter variance no larger than 0.0002 (diameters measured in inches). A random sample of 10 parts gives a sample variance of 0.0003.

1. Test, at the 5% level, H₀: σ² = 0.0002 against H₁: σ² > 0.0002.

2. Please construct 90% confidence interval for σ².